- [Instructor] Buffers consists of a significant amount
of a weak acid, which we will represent as HA
and the conjugate base to the weak acid,
which we will represent as A-.
Buffer solutions resist large changes in pH.
However, buffers are only effective
over a certain range of pH values.
We are going to use the Henderson-Hasselbalch equation
to find the effective pH range of a buffer.
Looking at the Henderson-Hasselbalch equation,
the pH of the buffer solution
is equal to the pKa of the weak acid,
which would be HA,
plus the log of the concentration of the conjugate base
divided by the concentration of the weak acid.
And it's this ratio of the concentration
of the conjugate base to the concentration of the weak acid
that determines if a buffer is effective or not.
Buffer solutions are most effective at resisting a change
in pH in either direction
when the concentration of the weak acid
is equal to the concentration of the conjugate base.
And when the concentrations are equal to each other,
the ratio is equal to one,
and the log of one is equal to zero.
Therefore, when the concentrations are equal to each other,
the pH of the buffer solution is equal to the pKa
of the weak acid plus zero.
So we could just say that the pH is equal to the pKa
when the concentration of the weak acid
is equal to the concentration of the conjugate base.
So we usually try to choose a buffer with a weak acid
that has a pKa value close to the desired pH
of the solution.
So buffers are effective at resisting large changes in pH
when the pH is approximately equal
to the pKa of the weak acid.
However, if the concentration of one component of a buffer
is more than 10 times the concentration
of the other component in a buffer,
buffers are not effective at resisting large changes to pH.
Therefore, to find the effective pH range,
we're gonna use the Henderson-Hasselbalch equation
to calculate the pH
when the concentration of the conjugate base
is 10 times the concentration of the weak acid,
and also to calculate the pH
when the concentration of the weak acid
is 10 times the concentration of the conjugate base.
Doing these two calculations
gives us the upper and lower limits
of the effective pH range.
So let's calculate the pH of the buffer solution
when the concentration of the conjugate base
is 10 times the concentration of the weak acid.
Looking at the Henderson-Hasselbalch equation,
if the concentration of the conjugate base
is 10 times the concentration of the weak acid,
the ratio is equal to 10 over one,
and the log of 10 is equal to one.
Therefore, the pH of the buffer solution
is equal to the pKa value of the weak acid plus one.
This value for the pH represents the upper limit
of the effective pH range.
Next, let's calculate the pH of the buffer solution
when the concentration of weak acid
is 10 times the concentration of the conjugate base.
Looking at the Henderson-Hasselbalch equation,
if the concentration of HA
is 10 times the concentration of A-,
the ratio is equal to one over 10,
and the log of one over 10 is equal to negative one.
Therefore, the pH of the buffer solution
is equal to the pKa value of the weak acid minus one.
This value for the pH represents the lower limit
of the effective pH range.
By the calculations that we've just done,
we've seen that the effective pH range of a buffer
is plus or minus one of the pKa value of the weak acid.
Let's use these concepts of an effective pH range
to choose a buffer solution.
Let's say we want to buffer a solution
at a pH of 9.00 at 25 degrees Celsius.
And suppose that we have two choices,
we could either choose an acetic acid-acetate buffer
or we could choose an ammonium-ammonia buffer.
Because the effective pH range of a buffer
is plus or minus one the pKa value of the weak acid,
we don't wanna choose
the acetic acid-acetate buffer solution.
Because at 25 degrees Celsius,
the pKa value for acetic acid is equal to 4.74.
Therefore, this buffer would only be effective
at a range of plus or minus one from 4.74,
so about 3.74 to approximately 5.74.
The ammonium cation has a pKa value equal to 9.25
at 25 degrees Celsius.
Therefore, the ammonium-ammonia buffer
is effective plus or minus one of this pKa value,
so approximately 8.25 to 10.25.
Since our pH of nine falls within that range,
we would choose the ammonium-ammonia buffer.